Is the ocean modifier better than the fluid simulation for making an ocean?
It really depends on the project you are undertaking.

For Oceans and Splashes
Any wave or developed ocean sim uses functions which are fractaly overlayed on top of each other (similar to Brownian Motion, Turbulence, etc), which produces a plausible in-the-middle-of-the-ocean effect. Note that ocean simulators by default DO NOT use any sort of fluid dynamics! As it has been mentioned in the comments, fluid dynamics is expensive and simulating a whole ocean using fluids is just something that is not done even in the VFX for your top-ten Hollywood films of last year.

Now, on the other hand splashes and sprinkles and water interacting with objects cannot be done plausibly with an ocean sim. You actually need fluid dynamics for that. 

What is usually done for a shot that has a huge CG ocean and water interacting with some object in the ocean (rocks, ships, kraken, huge robots, etc...) is that an ocean sim (or a few of them, different for foreground, midground and background [something like ocean LOD]) is used for the virgin ocean part of the shot, and a separate 'water-basin' is used where the interaction with the object happens. This is a limited container (as small as possible) with actually has 3d fluid dynamics, that are going to be used for the effects as splashes, droplets, etc.

The tricky part is here, you need to somehow combine the 2 techniques seamlessly!... Unfortunately there is no perfect solution which does not involve  manual tweaking of parameters for some time (There might be some tips I am not familiar with).

For Underwater Scenes
For such scenes, PLEASE, do not use fluid dynamics!!! Overkill is a weak word to use... it might even not produce the results you would expect! Now simulating the surface of the ocean with a ocean sim, and in the case of splashes and interaction, some fluid dynamics is fine (as we mentioned earlier). At the moment you get under those waves, it is just a completely different technique. There are quite alot of tutorials and techniques which teach realistic underwater effects.
Here are some basic ideas:
- You apply a 'depth' filter which would give the impression of this blue-ish foggy abyss.
- You combine that with tiny particles generated where they will be visible.
- Volumetric effect (similar to God-rays) for any lighting natural or man-made.
- particles for bubbles, racing to the surface...
- If you are close to the surface, you might want to apply caustic effects onto the objects which are visible...
- Last but not least use your observation and imagination! ;)